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为了解决共轭梯度法求解导热反问题过程中计算时间冗长、反演过程剧烈震荡等问题,基于有限元法建立了非迭代求解模型,并采用Fortran语言编制了相应的计算代码。将建立的数值模型应用于求解热轧钢板层流冷却过程的导热反问题,结果表明,非迭代方法能够获得较高精度的反演结果,计算时间较共轭梯度法减少了76%,且反演过程更加稳定。保留了矩阵的高度稀疏性,比已有的非迭代法更加简洁。此外,可同时反演出相应的热流密度和边界温度值,为热轧钢板层流冷却过程中热边界条件的实时输出提供了参考依据。
In order to solve the problem of lengthy calculation time and violent oscillation in the inverse heat conduction problem of conjugate gradient method, a non-iterative solution model was established based on finite element method and the corresponding calculation code was compiled by Fortran language. The numerical model is applied to the inverse problem of thermal conduction in the process of laminar cooling of hot-rolled steel. The results show that the non-iterative method can obtain the inversion results with higher precision, the calculation time is reduced by 76% compared with the conjugate gradient method, Play process more stable. It retains the high degree of sparsity of the matrix and is more concise than the existing non-iterative methods. In addition, the corresponding heat flux density and the boundary temperature can be inverted at the same time, which provides a reference for the real-time output of thermal boundary conditions in the process of laminar cooling.